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A346051
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G.f. A(x) satisfies: A(x) = 1 + x^2 + x^3 * A(x/(1 - x)) / (1 - x).
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3
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1, 0, 1, 1, 1, 2, 5, 12, 28, 68, 181, 531, 1671, 5491, 18627, 65299, 237880, 903907, 3580619, 14729777, 62639952, 274442521, 1236730244, 5729809348, 27292248240, 133614280479, 671803041553, 3464970976743, 18309428363425, 99010800275743, 547462187824465, 3093329527120022
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OFFSET
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0,6
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LINKS
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FORMULA
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a(0) = 1, a(1) = 0, a(2) = 1; a(n) = Sum_{k=0..n-3} binomial(n-3,k) * a(k).
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MATHEMATICA
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nmax = 31; A[_] = 0; Do[A[x_] = 1 + x^2 + x^3 A[x/(1 - x)]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[1] = 0; a[2] = 1; a[n_] := a[n] = Sum[Binomial[n - 3, k] a[k], {k, 0, n - 3}]; Table[a[n], {n, 0, 31}]
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PROG
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(Magma)
function a(n)
if n lt 3 then return (1+(-1)^n)/2;
else return (&+[Binomial(n-3, j)*a(j): j in [0..n-3]]);
end if; return a;
end function;
(SageMath)
@CachedFunction
if (n<3): return (1, 0, 1)[n]
else: return sum(binomial(n-3, k)*a(k) for k in range(n-2))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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